Suppose that I have an MIP with a whole lot of continuous variables and some integer variables. In my case, this takes a very long to solve (in fact I wasn't able at all to solve it to optimality). So I was wondering if it would be beneficial for solving this problem to exchange my integer variables by multiple binary variables.
The integer variables do have upper bounds in the range of $10^2$, so I would replace them with ~100 binary variables. Does this help my LP relaxation to get stronger? Actually, I would suggest to slightly adjust objective function coefficients, so I don't end up with ~100 variables of the exact same nature (I guess this might help).
I would appreciate any experience or expertise on this topic, Cheers.